Regularization of a Mathematical Model of the Wheatley Heart Valve.

This note considers the mathematical model published in the Journal of Biomechanical Engineering by McKee et al. [McKee, S., Cuminato, J. A., Stewart, I. W., and Wheatley, D. J., 2021, "A Mathematical Representation of the Wheatley Heart Valve," ASME J. Biomech. Eng., 143(8), p. 081006]. The model presented there suffers from the fact that there is a line discontinuity in the first derivative producing what appears to be a kink in each of the leaflets. This note is concerned with regularizing the shape of the valve while holding to Wheatley's essential idea [Wheatley, D. J., 2016, "Heart Valve," U.S. Patent No. 9,259,313, UK Patent No. 2,982,340 (2017), European Patent No. 2,979,666 (2017)].

A Mathematical Representation of the Wheatley Heart Valve.

Starting from a hand-drawn contour plot, this note develops a set of intersecting and contiguous circles whose perimeter, upon extending appropriately to three dimensions, can be seen to be a natural mathematical representation of the Wheatley heart valve.